20.–/4 pointslarpcalc8 2.6.060.my notes

question partpointssubmissions used

consider the following.

h(x) =  x2x  −  2 

(a) state the domain of the function.

all real numbers except  x  = 0all real numbers except  x  =  −2        all real numbers except  x  =  −2 and  x  = 2all real numbers except  x  = 2all real numbers

(b) identify all intercepts. (enter none in any unused answer blanks.)x-intercept        (x,  y)=(    ,    )y-intercept        (x,  y)=(    ,    )
(c) identify any vertical and slant asymptotes. (enter none if there is no asymptote.)vertical asymptote        x  =slant asymptote        y  =

 

(d) plot additional solution points as needed to sketch the graph of the rational function. 

    

21.–/4 pointslarpcalc8 2.6.070.mi. my notes

question partpointssubmissions used

use a graphing utility to graph the rational function. give the domain of the function and identify any asymptotes. then zoom out sufficiently far so that the graph appears as a line. identify the line. (enter none in any unused answer blanks.)

f(x) =  2x2  +xx  +  1 

domain:

all real numbersall real numbers  x  except  x  = 0        all real numbers  x  except  x  = 1all real numbers  x  except  x  =  −1all real numbers  x  except  x  =  −1 and  x  = 1

vertical asymptote          x  = 

 

slant asymptote          y  = 

 

line        y  = 

  utorial exercise

find a polynomial function with real coefficients that has the given zeros. (there are many correct answers.)

5,  −4i